In this study, we reanalyze the magnetic interactions in the Kitaev spin liquid candidate materials Na2IrO3, α-RuCl3, and α-Li2IrO3 using nonperturbative exact diagonalization methods. These methods are more appropriate given the relatively itinerant nature of the systems suggested in previous works. We treat all interactions up to third neighbours on equal footing. The computed terms reveal significant long range coupling, bond-anisotropy, and/or off-diagonal couplings which we argue naturally explain the observed ordered phases in these systems. Given these observations, the potential for realizing the spin-liquid state in real materials is analyzed, and synthetic challenges are defined and explained.

The layered honeycomb magnet α-RuCl3 has been proposed as a candidate to realize a Kitaev spin model with strongly frustrated, bond-dependent, anisotropic interactions between spin-orbit entangled j eff = 1/2 Ru 3+ magnetic moments. Here we report a detailed study of the three-dimensional crystal structure using x-ray diffraction on un-twinned crystals combined with structural relaxation calculations. We consider several models for the stacking of honeycomb layers and find evidence for a parent crystal structure with a monoclinic unit cell corresponding to a stacking of layers with a unidirectional in-plane offset, with occasional in-plane sliding stacking faults, in contrast with the currently-assumed trigonal 3-layer stacking periodicity. We report electronic band structure calculations for the monoclinic structure, which find support for the applicability of the j eff = 1/2 picture once spin orbit coupling and electron correlations are included. Of the three nearest neighbour Ru-Ru bonds that comprise the honeycomb lattice, the monoclinic structure makes the bond parallel to the b-axis non-equivalent to the other two, and we propose that the resulting differences in the magnitude of the anisotropic exchange along these bonds could provide a natural mechanism to explain the spin gap observed in powder inelastic neutron scattering [Banerjee et al.], in contrast to spin models based on the three-fold symmetric trigonal structure, which predict a gapless spectrum within linear spin wave theory. Our susceptibility measurements on both powders and stacked crystals, as well as magnetic neutron powder diffraction show a single magnetic transition upon cooling below TN ≈13 K. The analysis of our neutron powder diffraction data provides evidence for zigzag magnetic order in the honeycomb layers with an antiferromagnetic stacking between layers. Magnetization measurements on stacked single crystals in pulsed field up to 60 T show a single transition around 8 T for in-plane fields followed by a gradual, asymptotic approach to magnetization saturation, as characteristic of strongly-anisotropic exchange interactions.

Over the past few years Fe chalcogenides (FeSe/Te) have advanced to the forefront of Fe-based superconductors (FeBS) research. The most intriguing results thus far are for intercalated and monolayer FeSe, however experimental studies are still inconclusive. Yet, bulk FeSe itself remains an unusual case when compared with pnictogen-based FeBS, and may hold clues to understanding the more exotic FeSederivatives. The FeSe phase diagram is unlike the pnictides: the orthorhombic distortion, which is likely to be of a "spin-nematic" nature in numerous pnictides, is not accompanied by magnetic order in FeSe, and the superconducting transition temperature Tc rises significantly with pressure before decreasing. In this paper we show that the magnetic interactions in chalcogenides, as opposed to pnictides, demonstrate unusual (and unanticipated) frustration, which suppresses magnetic, but not nematic order, favors ferroorbital order in the nematic phase and can naturally explain the nonmonotonic pressure dependence of the superconducting critical temperature Tc(P ).While full consensus regarding the mechanism of hightemperature superconductivity in Fe-based superconductors (FeBS) remains elusive, nearly all researchers agree that it is unconventional and that it has a magnetic origin 1,2 . However, there is a divergence of opinions on the nature of the electrons responsible for magnetism. There is an itinerant approach based on calculating the spin susceptibility with moderate Coulomb (Hubbard) and Hund's interactions [3][4][5][6][7][8][9][10] as well as a localized approach where itinerant electrons responsible for conduction and the Fermi surface interact with local spins 11,12 . Finally, there is an increasingly popular description where the electrons have a dual character and provide the local moments, the interaction between them, and the electronic conductivity [13][14][15][16] . Within this picture, FeBS can still be reasonably mapped onto a short-range model of pairwise interactions between the local moments.Following the discovery of the FeBS, there were multiple attempts to map the exchange interactions onto the Heisenberg model. The J 1 -J 2 model on the square lattice 17 with nearest-(J 1 ) and next-nearest-neighbor (J 2 ) exchange couplings was a natural starting point 18-21 , but required dramatically different couplings for ferro-and antiferromagnetic neighbors, J 1a J 1b to reproduce the observed spin waves 22,23 and ab-initio calculations 24 ; it also failed to describe the double-stripe configuration in FeTe 25,26 . The model was extended to include third-neighbor exchange J 3 27 to reproduce the FeTe magnetic ground state. However, only the Ising model has this configuration as a solution, and in the Heisenberg model it is not a ground state for any set of parameters 28,29 . Therefore adding J 3 does not solve the problem. Besides, the J 1a J 1b implies an unphysical temperature dependence of the exchange constants (as T approaches T N , by symmetry J 1a → J 1b ).There were attempts to overcome these pr...

The discovery of a new family of high-T(C) materials, the iron arsenides (FeAs), has led to a resurgence of interest in superconductivity. Several important traits of these materials are now apparent: for example, layers of iron tetrahedrally coordinated by arsenic are crucial structural ingredients. It is also now well established that the parent non-superconducting phases are itinerant magnets, and that superconductivity can be induced by either chemical substitution or application of pressure, in sharp contrast to the cuprate family of materials. The structure and properties of chemically substituted samples are known to be intimately linked; however, remarkably little is known about this relationship when high pressure is used to induce superconductivity in undoped compounds. Here we show that the key structural features in BaFe2As2, namely suppression of the tetragonal-to-orthorhombic phase transition and reduction in the As-Fe-As bond angle and Fe-Fe distance, show the same behaviour under pressure as found in chemically substituted samples. Using experimentally derived structural data, we show that the electronic structure evolves similarly in both cases. These results suggest that modification of the Fermi surface by structural distortions is more important than charge doping for inducing superconductivity in BaFe2As2.

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